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ASIACRYPT
2003
Springer

Almost Uniform Density of Power Residues and the Provable Security of ESIGN

9 years 19 days ago
Almost Uniform Density of Power Residues and the Provable Security of ESIGN
Abstract. ESIGN is an efficient signature scheme that has been proposed in the early nineties (see [14]). Recently, an effort was made to lay ESIGN on firm foundations, using the methodology of provable security. A security proof [15] in the random oracle model, along the lines of [2], appeared in support for ESIGN. However, several unexpected difficulties were found. Firstly, it was observed in [20], that the proof from [15] holds in a more restricted model of security than claimed. Even if it is quite easy to restore the usual security level, as suggested in [9], this shows that the methodology of security proofs is more subtle than it at first appears. Secondly, it was found that the proof needs the additional assumption that e is prime to ϕ(n), thus excluding the case where e is a small power of two, a very attractive parameter choice. The difficulty here lies in the simulation of the random oracle, since it relies on the distribution of e-th powers, which is not completely und...
Tatsuaki Okamoto, Jacques Stern
Added 06 Jul 2010
Updated 06 Jul 2010
Type Conference
Year 2003
Where ASIACRYPT
Authors Tatsuaki Okamoto, Jacques Stern
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